\begin{abstract}


Fundamental local symmetry breaking  problems such as Maximal Independent Set (MIS) and coloring have been recognized as important by the community, and studied extensively in (standard) graphs. In particular, fast (i.e., logarithmic run time)   randomized algorithms are well-established for MIS and $\Delta +1$-coloring in both the LOCAL and CONGEST distributed computing models.  On the other hand, comparatively much less is known on the complexity of distributed symmetry breaking in {\em hypergraphs}.
In particular,  a key question is  whether a fast (randomized) algorithm for MIS exists  for hypergraphs.

In this paper, we study the distributed complexity of symmetry breaking in hypergraphs   by presenting distributed randomized algorithms for a variety of fundamental problems under a natural distributed computing model for hypergraphs.    We first show that MIS in hypergraphs (of arbitrary dimension) can be solved in $O(\log^2 n)$ rounds  ($n$ is the number of nodes of the hypergraph) in the LOCAL  model. 
We then present a key result of this paper ---  an $O(\Delta^{\eps}\polylog n)$-round   hypergraph MIS algorithm in the CONGEST model  where  $\Delta$ is the maximum node degree of the hypergraph and
$\eps > 0$ is any arbitrarily small constant. We also present distributed algorithms for coloring, maximal matching, and maximal clique in hypergraphs.

To demonstrate the usefulness 
of hypergraph MIS, we present applications of our hypergraph algorithm to solving problems in (standard) graphs.
In particular, the hypergraph MIS yields fast distributed algorithms for the  {\em balanced minimal dominating set} problem (left open in Harris et al. [ICALP 2013]) and the {\em minimal connected dominating set  problem}.  

Our work shows that while some local symmetry breaking problems such as coloring can be solved in polylogarithmic rounds in both the LOCAL and CONGEST models, for many other hypergraph problems  such as MIS, hitting set, and maximal clique, it remains challenging to obtain polylogarithmic time algorithms in the CONGEST model.  This work is a step towards understanding this dichotomy in the complexity of hypergraph problems as well
as using hypergraphs to design fast distributed algorithms for problems in (standard) graphs.

\end{abstract}

